reserve A for non empty set,
  a for Element of A;
reserve A for set;
reserve B,C for Element of Fin DISJOINT_PAIRS A,
  x for Element of [:Fin A, Fin A:],
  a,b,c,d,s,t,s9,t9,t1,t2,s1,s2 for Element of DISJOINT_PAIRS A,
  u,v,w for Element of NormForm A;
reserve K,L for Element of Normal_forms_on A;
reserve f,f9 for (Element of Funcs(DISJOINT_PAIRS A, [:Fin A,Fin A:])),
  g,h for Element of Funcs(DISJOINT_PAIRS A, [A]);

theorem Th24:
  u "/\" StrongImpl(A).(u, v) [= v
proof
  now
    let a;
    assume
A1: a in u "/\" StrongImpl(A).(u, v);
A2: @(StrongImpl(A).(u, v)) = mi(@u =>> @v) by Def9;
    u "/\" StrongImpl(A).(u, v) = M(A).(u, StrongImpl(A).(u, v)) by
LATTICES:def 2
      .= mi(@u ^ mi(@u =>> @v)) by A2,NORMFORM:def 12
      .= mi(@u ^ (@u =>> @v)) by NORMFORM:51;
    then a in @u ^ (@u =>> @v) by A1,NORMFORM:36;
    hence ex b st b in v & b c= a by Lm6;
  end;
  hence thesis by Lm3;
end;
